STAGE 6 MATHEMATICS 2/3 UNIT TOPICS

TOPIC 2 UNIT COURSE 3 UNIT COURSE Basic Arithmetic and

Algebra

Basic number Inequalities with unknown in denominator

Surds

Absolute value – evaluation, equations, inequalities

Basic algebra

Factorising

Equations – basic, quadratic, simultaneous

Inequalities – linear, quadratic

Plane Geometry Angles

Parallel lines

Triangles

Quadrilaterals

Congruency

Similarity

Pythagoras’ theorem

Areas

Functions and

Relations

Function notation

Domain and range

Sketching functions

Even and odd functions

Sketching regions involving inequalities

Circle Geometry Arcs and cords

Angle properties

Chord properties

Cyclic Quadrilaterals

Tangent properties

TOPIC 2 UNIT COURSE 3 UNIT COURSE Differentiation Limits

First principles

𝑑

𝑑𝑥 𝑥𝑛

Product rule

Quotient rule

Functions of a function rule

Gradients of tangents and normals

Equations of tangents and normals

Trigonometry Right angled trigonometry Sum and difference formulae

Reciprocal ratios Double angle formulae

Complementary ratios t-formulae

Exact values Complicated equations

Angles of any magnitude

Sine rule

Cosine rule

Area of a triangle

Pythagorean identities

Trigonometric ratios

Quadratic Functions Sketching quadratics

Quadratic functions – by factors, by formula, by completing the

square

Discriminant

Roots of quadratic equations

Quadratic identities

Equations reducible to quadratics

Coordinate Geometry Distance formula Angle between two lines

Gradient formula Dividing interval in given ratio

Midpoint formula, m = tanƟ

Equations of straight lines

Parallel and perpendicular lines

TOPIC 2 UNIT COURSE 3 UNIT COURSE Polynomials Definition of polynomial

Graphing polynomial

Remainder and factor theorem

Relationship between coefficients and roots

Determining roots by halving the interval

Determining roots by Netwon’s Method

Parabola Locus Parametric form of parabola

Parts or parabola Equations of tangents and normals

x2 = 4ay Equation of chord of contact

(x – h)2 = 4a (y – k) Locus problems

Geometric application

of Differentiation

Significance of f’(x) and f” (x) Curve stretching with curves with asymptotes

Sketching derivative curves

Stationary points

Increasing and decreasing curves

Concavity

Inflexion points

Curve sketching

Maxima and minima problems

Primitive functions

Series and their

Applications

Indices Mathematical induction

Logarithms

Definition of term, nth term, sum to n terms, sigma notation

AP’s

GP’s

Limiting sum

Problems with AP’s and GP’s

Repeating decimals

Compound interest

Superannuation

Time payments

TOPIC 2 UNIT COURSE 3 UNIT COURSE Integration Trapezoidal rule Integration by substitution

Simpson’s rule

Indefinite integrals

Definite integrals

Area under curves

Volumes of revolution

Trigonometric

Functions

Radians Integration

Arc length Solving harder trigonometric equations

Area of sector Integration involving double angle formula

Area of minor segment

Graphics of trigonometric functions

Differentiation of trigonometric functions

Integration of trigonometric functions

Area of volumes involving trigonometric functions

Solving trigonometric functions

Exponential and

Logarithmic

Functions

y = ex

Graphs of exponential functions

Differentiation and integration of exponentials

Areas and volumes involving exponentials

y = logex

Graphs of logarithmic functions

Differentiation of logarithmic functions

Integration of functions resulting in log functions

Area and volumes involving log functions

Inverse Functions Inverse functions

Graphs of inverse functions

Inverse trigonometric functions

Differentiating inverse trigonometric functions

Integrals involving inverse trigonometric functions

Areas and volumes

TOPIC 2 UNIT COURSE 3 UNIT COURSE Binomial Theorem Pascal’s triangle

Properties of combinations

Expanding binomial products

Relationship between binomial coefficients

Probability Simple events Permutations

Complementary events Combinations

Product theorem Permutations and combinations and probability**

Addition theorem Probability using binomial theorem**

Application of

Calculus to the

Physical World

Rates of change* Motion as derivatives or integrals relating to x

Exponential Growth and Decay* Simple harmonic motion

Motion as derivatives or integrals relating to time* Projectiles**

Note: sections with * will be tested in the Extension 1 paper for the trial examination

**will not be tested in the trial examination